We consider a memoryless source \(X\in \mathcal {X}\)  with reproduction \(Y\in \mathcal {Y}\) , where \(\mathcal {X}=\lbrace x_1,\cdots ,x_M\rbrace , \mathcal {Y}=\lbrace y_1,\cdots ,y_N\rbrace \)  are finite and discrete alphabets.
Given a marginal distribution \(P_{X}\in \mathcal {P}_{\mathcal {X}}\)  and a distortion measure \(d:\mathcal {X}\times \mathcal {Y}\rightarrow \mathbb {R}^{+}\) , the classical RD function is defined as [1]}, [2]},
\(R(D):=\min _{W(y \mid x): \sum _{x,y} P_{X}(x) W(y \mid x) d(x, y) \le D} I(X ; Y).\) 
